In my opinion, after shooting sixteen different brands of plywood over a period of thirty years, the .416 Rigby is noticeably more effective than the .375 H&H, although a .375 Weatherby is nearly as effective as the .416. It doesn't hurt, however, to have a stopping double rifle when shooting plywood because of the advantages of having two aimed shots without without need to manually reload. The bigger bore and heavier bullet also practically guarantees penetration so long as an adequate bullet is used. I prefer the Barnes solids when I'm using my .470 plywood rifle.
Today's plywood is simply tougher than the plywood than was shot 50 years ago. The 375H&H has become, in my opinion, a marginal caliber for 1" plywood. Mind you, although it is marginal, the venerable H&H remains on the right side of the margin. I can honestly say that I have never had to follow up a wounded sheet of plywood after shooting it with anything heavier than the .375 H&H. My recommendation is to pick one of the .416s.